# Some explicit identities associated with positive self-similar Markov processes.

Abstract : We consider some special classes of Lévy processes with no gaussian component whose Lévy measure is of the type $\pi(dx)=e^{\gamma x}\nu(e^x-1)\,dx$, where $\nu$ is the density of the stable Lévy measure and $\gamma$ is a positive parameter which depends on its characteristics. These processes were introduced in \cite{CC} as the underlying Lévy processes in the Lamperti representation of conditioned stable Lévy processes. In this paper, we compute explicitly the law of these Lévy processes at their first exit time from a finite or semi-finite interval, the law of their exponential functional and the first hitting time probability of a pair of points.
Keywords :
Type de document :
Pré-publication, Document de travail
2007
Domaine :

https://hal.archives-ouvertes.fr/hal-00167291
Contributeur : Juan Carlos Pardo Millan <>
Soumis le : vendredi 17 août 2007 - 17:30:52
Dernière modification le : vendredi 16 novembre 2018 - 01:53:20
Document(s) archivé(s) le : vendredi 9 avril 2010 - 00:54:22

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### Identifiants

• HAL Id : hal-00167291, version 1
• ARXIV : 0708.2383

### Citation

Loic Chaumont, Andreas Kyprianou, Juan Carlos Pardo Millan. Some explicit identities associated with positive self-similar Markov processes.. 2007. 〈hal-00167291〉

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